Question 313459
The oldest child in a family of four children is twice as old as the youngest.
 The two middle children are 13 and 15 years old.
 If the average age of the children is 14.5, how old is the youngest child?
:
Let x = the youngest child
then
2x = the oldest child
:
"the average age of the children is 14.5,"
{{{(x + 13 + 15 + 2x)/4}}} = 14.5
:
{{{(3x + 28)/4}}} = 14.5  
Multiply both sides by 4
3x + 28 = 4(14.5)
3x + 28 = 58
3x = 58 - 28
3x = 30
x = {{{30/3}}}
x = 10 yrs is the youngest child
:
:
Check solution (oldest child = 20)
{{{(10 + 13 + 15 + 20)/4}}} =
{{{58/4}}} = 14.5